Not only in such a practical affair as insurance, but in matters purely scientific, the minute and subtle peculiarities of individuals have important consequences.  Each man has a certain cast of mind, character, physique, giving a distinctive turn to all his actions even when he tries to be normal.  In every employment this determines his Personal Equation, or average deviation from the normal.  The term Personal Equation is used chiefly in connection with scientific observation, as in Astronomy.  Each observer is liable to be a little wrong, and this error has to be allowed for and his observations corrected accordingly.

The use of the term ‘expectation,’ and of examples drawn from insurance and gambling, may convey the notion that probability relates entirely to future events; but if based on laws and causes, it can have no reference to point of time.  As long as conditions are the same, events will be the same, whether we consider uniformities or averages.  We may therefore draw probable inferences concerning the past as well as the future, subject to the same hypothesis, that the causes affecting the events in question were the same and similarly combined.  On the other hand, if we know that conditions bearing on the subject of investigation, have changed since statistics were collected, or were different at some time previous to the collection of evidence, every probable inference based on those statistics must be corrected by allowing for the altered conditions, whether we desire to reason forwards or backwards in time.

Sec. 7.  The rules for the combination of probabilities are as follows: 

(1) If two events or causes do not concur, the probability of one or the other occurring is the sum of the separate probabilities.  A die cannot turn up both ace and six; but the probability in favour of each is 1/6:  therefore, the probability in favour of one or the other is 1/3.  Death can hardly occur from both burning and drowning:  if 1 in 1000 is burned and 2 in 1000 are drowned, the probability of being burned or drowned is 3/1000.

(2) If two events are independent, having neither connection nor repugnance, the probability of their concurring is found by multiplying together the separate probabilities of each occurring.  If in walking down a certain street I meet A once in four times, and B once in three times, I ought (by mere chance) to meet both once in twelve times:  for in twelve occasions I meet B four times; but once in four I meet A.

This is a very important rule in scientific investigation, since it enables us to detect the presence of causation.  For if the coincidence of two events is more or less frequent than it would be if they were entirely independent, there is either connection or repugnance between them.  If, e.g., in walking down the street I meet both A and B oftener than once in twelve times, they may be engaged in similar business, calling them from their offices at about the same hour.  If I meet